/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) Strip Symbols Proof [SOUND, 0 ms] (2) QTRS (3) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms] (4) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: b(a(a(b(a(b(a(a(a(b(x1)))))))))) -> a(b(a(b(a(a(a(b(a(b(a(a(b(x1))))))))))))) Q is empty. ---------------------------------------- (1) Strip Symbols Proof (SOUND) We were given the following TRS: b(a(a(b(a(b(a(a(a(b(x1)))))))))) -> a(b(a(b(a(a(a(b(a(b(a(a(b(x1))))))))))))) By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: b(a(a(b(a(b(a(a(a(x))))))))) -> a(b(a(b(a(a(a(b(a(b(a(a(x)))))))))))) ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: b(a(a(b(a(b(a(a(a(x))))))))) -> a(b(a(b(a(a(a(b(a(b(a(a(x)))))))))))) Q is empty. ---------------------------------------- (3) RFCMatchBoundsTRSProof (EQUIVALENT) Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 2. This implies Q-termination of R. The following rules were used to construct the certificate: b(a(a(b(a(b(a(a(a(x))))))))) -> a(b(a(b(a(a(a(b(a(b(a(a(x)))))))))))) The certificate found is represented by the following graph. The certificate consists of the following enumerated nodes: 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168 Node 123 is start node and node 124 is final node. Those nodes are connected through the following edges: * 123 to 125 labelled a_1(0)* 124 to 124 labelled #_1(0)* 125 to 126 labelled b_1(0)* 126 to 127 labelled a_1(0)* 127 to 128 labelled b_1(0)* 128 to 129 labelled a_1(0)* 129 to 130 labelled a_1(0)* 130 to 131 labelled a_1(0)* 131 to 132 labelled b_1(0)* 131 to 147 labelled a_1(1)* 132 to 133 labelled a_1(0)* 133 to 134 labelled b_1(0)* 133 to 136 labelled a_1(1)* 134 to 135 labelled a_1(0)* 135 to 124 labelled a_1(0)* 136 to 137 labelled b_1(1)* 137 to 138 labelled a_1(1)* 138 to 139 labelled b_1(1)* 139 to 140 labelled a_1(1)* 140 to 141 labelled a_1(1)* 141 to 142 labelled a_1(1)* 142 to 143 labelled b_1(1)* 142 to 158 labelled a_1(2)* 143 to 144 labelled a_1(1)* 144 to 145 labelled b_1(1)* 144 to 136 labelled a_1(1)* 145 to 146 labelled a_1(1)* 146 to 124 labelled a_1(1)* 147 to 148 labelled b_1(1)* 148 to 149 labelled a_1(1)* 149 to 150 labelled b_1(1)* 150 to 151 labelled a_1(1)* 151 to 152 labelled a_1(1)* 152 to 153 labelled a_1(1)* 153 to 154 labelled b_1(1)* 153 to 158 labelled a_1(2)* 154 to 155 labelled a_1(1)* 155 to 156 labelled b_1(1)* 155 to 136 labelled a_1(1)* 156 to 157 labelled a_1(1)* 157 to 142 labelled a_1(1)* 158 to 159 labelled b_1(2)* 159 to 160 labelled a_1(2)* 160 to 161 labelled b_1(2)* 161 to 162 labelled a_1(2)* 162 to 163 labelled a_1(2)* 163 to 164 labelled a_1(2)* 164 to 165 labelled b_1(2)* 164 to 158 labelled a_1(2)* 165 to 166 labelled a_1(2)* 166 to 167 labelled b_1(2)* 166 to 136 labelled a_1(1)* 167 to 168 labelled a_1(2)* 168 to 142 labelled a_1(2) ---------------------------------------- (4) YES